Pre-2APre-2BPre-2CPre-2DAre you ready for Beast Academy 2A?© 2017, AoPS Incorporated.A student ready for Beast Academy 2A should be able to answer at least 13 of the 17 problems below correctly.Before beginning Beast Academy 2A, a student should be able to count beyond 100 by 1’s, 5’s, and 10’s.Step 1. The student should try to answer every question without a calculator and without help. Step 2. Check the student’s answers using the solutions at the end of this document.Step 3. The student should be given a second chance on problems answered incorrectly.The student should also know basic shapes, be able to add and subtract numbers from 1 to 20, and be able to solve simple word problems. Fill the blanks to complete each counting pattern below.1. 1, 2, 3, 4, ____, ____, ____, 8, ____, ____, ____2. ____, ____, ____, 22, 23, ____, 25, 26, ____, ____, 29, ____4. 5, 10, 15, 20, ____, ____, ____, ____, ____, 505. ____, ____, 75, 80, 85, ____, 95, _____3. 10, 20, 30, ____, 50, 60, ____, ____, ____, 100 Answer each question about the shapes shown below.6. How many circles are there?7. How many more circles are there than squares?6. ________7. ________Are you ready for Beast Academy 2A?© 2017, AoPS Incorporated. Fill the blanks in each problem below.8. 2+7=_____ Solve each problem below. 14. Mike puts 6 pennies in an empty jar. Nelly puts 7 more pennies in the jar. Orson takes all of the pennies out of the jar. How many pennies does Orson take?15. There are 3 boys and 6 girls in Mr. Hai’s class. How many pencils are needed to give each student in Mr. Hai’s class two pencils?14. ________15. ________9. 8+12=_____ 10. 4+_____=1111. 9−6=_____ 12. 17−8=_____ 13. _____−13=616. Fill each blank with the same number in the addition problem below. _____+_____+_____=1817. Fill the empty squares below so that the numbers in each row (left to right) and each column (top to bottom) add up to 20.8 4511Are you ready for Beast Academy 2A?© 2017, AoPS Incorporated.1. Counting by ones, we have1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.2. Counting by ones, we have19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.3. Counting by tens, we have10, 20, 30, 40, 50, 60, 70, 80, 90, 100.4. Counting by fives, we have5, 10, 15, 20, 25, 30, 35, 40, 45, 50.5. Counting by fives, we have65, 70, 75, 80, 85, 90, 95, 100.6. We see two groups of 5 circles, plus a circle at each end.Two groups of 5 is 10, and plus 2 more is 12. So, there are 12 circles.7. In the previous problem, we counted 12 circles. We also count 9 squares. So, there are 12−9=3 more circles than squares.8. 2+7=9.9. 8+12=20.10. 4+7=11.11. 9−6=3.12. 17−8=9.13. 19−13=6.14. Together, Mike and Nelly put 6+7=13 pennies into the jar. Orson takes all of the pennies. So, Orson takes 13 pennies.15. All together, there are 3+6=9 students in Mr. Hai’s class. Each of the 9 students gets 2 pencils. So, we add nine 2’s to get the total number of pencils needed:2+2+2+2+2+2+2+2+2=18. or Adding nine 2’s is the same as adding two 9’s. So, 9+9=18 pencils are needed.16. We start by trying a number that is easy to add, such as 5. Adding three 5’s gives5+5+5=15.15 is too small, so we try adding a larger number. Adding three 6’s gives6+6+6=18.This is the correct result! So, we fill each blank with 6.17. In the top row, we have 8 and 4. We know 8+4=12. Since 12+8=20, the missing number in the top row is 8.8 8 4511In the left column, we have 8 and 5. We know 8+5=13. Since 13+7=20, the missing number in the left column is 7.8 8 457 11In the bottom row, we have 7 and 11. We know 7+11=18. Since 18+2=20, the missing number in the bottom row is 2.8 8 457 2 11In the middle column, we have 8 and 2. We know 8+2=10. Since 10+10=20, the missing number in the middle column is 10.8 8 45 107 2 11In the middle row, we have 5 and 10. We know 5+10=15. Since 15+5=20, the missing number in the middle row is 5.8 8 45 10 57 2 11SolutionsAre you ready for Beast Academy 2B?© 2018, AoPS Incorporated.A student ready for Beast Academy 2B should be able to answer at least 14 of the 18 problems below correctly.Before beginning Beast Academy 2B, students should be fluent with place value, number lines, and the comparison symbols < and >.Step 1. The student should try to answer every question without a calculator and without help. Step 2. Check the student’s answers using the solutions at the end of this document.Step 3. The student should be given a second chance on problems answered incorrectly.Students should also be able to add 2-digit and 3-digit numbers without stacking by using place value or other mental strategies. Fill in the blanks to complete the statements below.1. Circle every number below whose ones digit is larger than its hundreds digit.675 567 756 576 765 6572. 4 tens and 13 ones is the same as 5 tens and _____ ones.3. 34 tens is the same as _____ hundreds and 4 tens. Label the missing numbers on each number line below.4. 5. 40 45100 200Are you ready for Beast Academy 2B?© 2018, AoPS Incorporated.6. 87 78 Solve each problem below. 7. 60+6 70−7 8. 29 ones 3 tens9. 43+56=_____ 10. 215+340=_____ 11. 27+44=_____ Fill in the blanks to complete each sum below. Fill each circle below with < or >.12. 397+65=_____ 13. 626+99=_____ 14. 444+ _____=87616. Juan doubles a number, then doubles the result and gets 140. What number did Juan start with?16. ________15. What is the sum of every whole number from 21 to 29?15. ________17. Fill each blank below with a number using only the digits 5 and 8.55 < ______ < 85 < 88 < ______ < 558 < ______ < ______ < 85518. In the Sum Pyramid below, each block contains the sum of the two numbers below it. Fill each empty block with the correct number.500195190Are you ready for Beast Academy 2B?© 2018, AoPS Incorporated.1. For any three-digit number, the hundreds digit is the leftmost digit, followed by the tens digit, then the ones digit.OnesTensHundredsWe circle each number below whose ones digit is larger than its hundreds digit.675 567 756 576 765 6572. We can regroup 13 ones to make 1 ten and 3 ones. So, 4 tens and 13 ones is the same as 5 tens and 3 ones.=3. We can regroup 10 tens to make 1 hundred. =Since 34=10+10+10+4, we can regroup 34 tens to make 3 hundreds, with 4 tens left over. So, 34 tens is the same as 3 hundreds and 4 tens.4.